In such questions of quantitative comparison, always first simplify the two quantities as below:

Quantity A: \(2x^2\) - 7x - 3
Quantity B: \(5x^2\) + x - 3

First, you can add 3 on both quantities, because it will not change the answer. i.e if a quantity is greater, after addition or subtraction by same number to both quantities, the greater quantity will remain greater. Also if both quantities are equals, the addition and subtraction has no effect, and both will remain equal after adding or subtracting same number to both quantities.

Thus, after adding 3 and 7x to both quantities,

Quantity A: \(2x^2\)
Quantity B: \(5x^2\) + 8x

Now, similarly, we can subtract \(2x^2\) from both quantities and get,

Quantity A: 0
Quantity B: \(3x^2\) + 8x

Now, at this point, again you don't need to plugin. Just you need to think and use common sense here:

\(3x^2\) is either 0 or positive. If x is 0, which can be possible, then the two quantities becomes equal. Otherwise, if x positive, then Quantity B is greater. And if x is negative, then Quantity A become greater.

Thus, Choice D is correct.